Non-overlapping domain decomposition

method based on the surface Calderon-Ryaben’kii’s potentials

Our approach is to formulate it as an inverse problem and perform multiple calculations. To carry out the computations in a reasonable time and with reasonable accuracy, near-wall domain decomposition is implemented. This is based on the construction of interface nonlocal boundary conditions which replace the solution in the inner near-wall region.

The method

An original approach to non-overlapping decomposition is being developed by Dr Sergey Utyuzhnikov. The method is based on the surface Calderon-Ryaben’kii’s potentials. The key advantage of the approach is an opportunity to generate a mesh in each sub-region independently. This allows us to avoid any projection of the solution on one mesh onto another one. Different regions are linked with each other via interface boundary conditions which are formulated as pseudo-differential boundary equations.

In the algorithm a computational region can be significantly reduced. The solution in the rest region can be replaced by an interface nonlocal boundary equation. The technology is applied to two problems of stress analysis and fluid dynamics led by Dr Utyuzhnikov.

Applications

One of the projects is devoted to the identification of leak before break in pipes. It is being carried out by Wiliam Woodward, a PhD student co-supervised at EDF R+D by Dr Patrick Massin. In the project, the difference potential method (DPM) is used for the reduction of a computational region around a possible crack and efficient solution of the governing equations.

Another project is related to near-wall turbulence modelling. The project title is "Numerical simulation of flows in gas-cooled nuclear reactor cores with uncertainties in surface geometry" and is being conducted by Adam Jones who is an EngD student. The EDF co-supervisors are Professor Dominique Laurence and Dr Jim Gotts.  The project involves numerical modelling of turbulent flows around walls with an undetermined roughness.

1. Utyuzhnikov S V. 2006. "The Method of Boundary Condition Transfer in Application to Modeling Near-Wall Turbulent Flows". Computers and Fluids. Vol. 35. Issue 10. pp 1193-1204. DOI: 10.1016/j.compfluid.2005.05.005
2. Utyuzhnikov S V. 2008. "Robin-type wall functions and their numerical implementation". Applied Numerical Mathematics. Vol. 58. Issue 10. pp 1521-1533. October. DOI: 10.1016/j.apnum.2007.09.003
3. Utyuzhnikov S V. 2009. "Domain decomposition for near-wall turbulent flows". Computers and Fluids. Vol. 38. Issue 9. pp 1710-1717. DOI: 10.1016/j.compfluid.2009.03.003
4. Utyuzhnikov S V. 2009. "Generalized Calderon - Ryaben'kii's Potentials". IMA Journal of Applied Mathematics. Vol. 74. Issue 1. pp 128-148. February. DOI: 10.1093/imamat/hxn025
5. Utyuzhnikov S V. 2009. "Active Wave Control and Generalized Surface Potentials". Advances in Applied Mathematics. Vol. 43. Issue 2. pp 101-112. DOI: 10.1016/j.aam.2008.12.001
6. Utyuzhnikov S V. 2010. "Nonlinear Problem of Active Sound Control". Journal of Computational and Applied Mathematics. Vol. 234. Issue 1. pp 215-223. DOI: 10.1016/j.cam.2009.12.017
7. Utyuzhnikov S V. 2012. "Interface Boundary Conditions in Near-wall Turbulence Modeling". Computers and Fluids. Vol. 68. pp 186-191. DOI: 10.1016/j.compfluid.2012.07.023